Peaksigmoid: Difference between revisions

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===Synopsis===
===Synopsis===


:[i0,iw] = peakfind(x,width,tolfac,w,options)
:[y,y1,y2] = peaksigmoid(x,p)
:[i0,iw] = peakfind(x,width,options)


===Inputs===


====Inputs====
* '''x''' = 3 element vector where
:* x(1) = coefficient
:* x(2) = offset
:* x(3) = decay constant
* '''p''' = axis 1xN  (# of independent variables)


* '''x''' =   3 element vector where x(1) = coefficient, x(2) = offset and x(3) is equal to the decay constant
===Outputs===




====Outputs====
* '''y(1) ''' = <math> {{x}_{1}} \left( \frac{1-{{\operatorname{e}}^{-z}}}{{ 1 }+{{\operatorname{e}}^{-z}}} \right)</math> where z = <math> {x}_{3}\left(p -{x}_{2} \right)</math>, 1xN
* '''y(2)  '''  = <math>{\operatorname{d}\!y\over\operatorname{d}\!{x}_{i}}</math> , 3xN


|-
* ''' y(3)  '''  = <math>{\operatorname{d^2}\!y\over\operatorname{d}\!{{x}_{i}}^{2}}</math> , 3x3xN
| <source lang="latex" enclose="none">dt, \operatorname{d}\!t, \partial t, \nabla\psi</source>
 
| <math>dt, \operatorname{d}\!t, \partial t, \nabla\psi\!</math>
===See Also===
|-
 
| <source lang="latex" enclose="none">dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y </source>
[[peakfunction]], [[peakexponential]], [[peakgaussian]], [[peaklorentzian]], [[peakpvoigt1]], [[peakpvoigt2]]
| <math>dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!</math>
|-
| <source lang="latex" enclose="none">\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y </source>
| <math>\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y</math>
|-
!colspan="2"|

Latest revision as of 10:05, 23 May 2023

Purpose

Outputs a sigmoid function.


Synopsis

[y,y1,y2] = peaksigmoid(x,p)

Inputs

  • x = 3 element vector where
  • x(1) = coefficient
  • x(2) = offset
  • x(3) = decay constant
  • p = axis 1xN (# of independent variables)

Outputs

  • y(1) = where z = , 1xN
  • y(2) = , 3xN
  • y(3) = , 3x3xN

See Also

peakfunction, peakexponential, peakgaussian, peaklorentzian, peakpvoigt1, peakpvoigt2

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